Good evening ma'am/sir;

Can you help me with this problem? It's a problem from the book of Algebra by Thomas Hungerford and it is located in Chapter III: Section 4(RINGS OF QUOTIENTS AND LOCALIZATION), EXERCISE's NO. 3. What I need is, the detailed proof of the problem. Also, is it possible if you can please provide reasons by line in order for me to understand the proof? BIG THANKS in advance. :)

3. (a) The set E of positive even integers is a multiplicative subset of Z such that E-1(Z) is the field of rational numbers. (b) State and prove condition(s) on a multiplicative subset S of Z which insure that S-'Z is the field of rationals